In this paper we consider a new technique to evaluate the Source-to-terminal Diameter Constrained Network reliability of a communication network. This reliability model is a generalization of the classical reliability and it was defined in order to reflect performance objectives of a network in which the quality of the communication depends on the existence of short-enough paths connecting a set of distinguished set of terminal vertices. Although the general problem is NP-hard, we propose an exact evaluation recursive method based on the inclusion-exclusion principle and topological reductions of a network and we show numerical illustrations to reflect the computational gain offered in comparison to other predominantly used evaluation techniques.